Circuits for passing or stopping a frequency band of alternating currents



Dec. 14, 1926. 1,610,336

J. S. STONE CIRCUITS FOR PASSING OR STOPPING A FREQUENCY BAND OF ALTERNATING CURRENTS Filed Nov. 50, 1920 3 Sheets-Sheet 1 Admihzmce for lm aenda nee of /2 branches /8 loops lmpenaoncefbr 6 branches Admittance far 6 ZOO/OS Susce aiance f r 6 firancive 5 Feaciaflre f0 6 100 5 fecx orocal BY W ATTORNEY Deec l4 1926. 1,610,336

J. s. STONE CIRCUITS FOR PASSIN3 OR STOPPING A FREQUENCY BAND OE ALTERNATING CURRENTS Filed Nov. 50, 1920 3 Sheets-Sheet 2 Adm ifiance V of Smsoeyaibnce for 6 branches Eeaczance 6 Zoo 5 Susce fence for Eeaciance for lE/aa 95 x Susce 'iance for brancires/ C'orzdu dance, for lffiramilfies/stance feacf'awc e. 077 czrczaz" Fe acfance INVENTOR W AI IORNEY Deco 14, E926.

J. S. STONE CIRCUITS FOR PASSING OR STOPPING A FREQUENCY BAND OF ALTERNATING cURRENTs 3 Sheets-Sheet 3 Filed Nov. 30, 1920 e/emenia] Zoo vs 20y etizer? m Q H mm m T O mw n V0.0 A W W IHr f2 Patented Dec. 14, 1926.

warren stares PATENT @FFHQE.

JOHN STONE STONE, OF SAN DIEGO, CALIFORNIA, ASSIGNOR TO AMERICAN TELE PHONE AND TELEGRAPH COIVIPANY, A COBPORATTON OF NEVT YORK.

CIRCUITS FOR PASSING OR STOPPING- A FREQUENCY BAND OF ALTERNATING CURRENTS.

Application filed November It is an object of my invention to provide a network that shall have predetermined characteristics as to its circuitfunctions between two defined limits of frequency of the current traversing it. The term circuit functions includes the well known functions of impedance, admittance, resistance, conductance. reactance and susceptance.

Another object of my invention is to provide a new and improved system of circuits that shall effectively pass (or stop) currents of frequency between certain lnnitsgbut stop (or pass) currents outside those limits. Another object of my invention is to provide a system of circuits that shall offer a high (or low) impedance to currents of a certain frequency range, but low (or high) impedance to currents of frequencies outside that range. Such circuits find useful applications in many situations; for example, in multiplex telephone work where, in some cases, it is desired to admit to certain apparatus only currents within a certain frequency range, and, in ther cases, efiectively to bar out from the apparatus currents within a certaln frequency range. Y I

Referring to the drawings, Figure 1 1s a diagram illustrating a system of circuits for offering low impedance to a frequency band and relatively high impedance to frequencies outside that band; Fig. 2 is a diagram illustrating a system designed to bar currents within a certain frequency band while passing currents of frequencies outside that band; Figs. 3, 4 and 5 are characterisuc diagran'ls for the apparatus illustrated in n'igs.

'1' and 2; Fig. 6 is a diagram of amodification, a band reactance neutralizer of one loop; Fig. 7 is a characteristic diagram for the apparatus of Fig. 6; Fig. 8 is a diagram of a band reactance neutralizer of three loops; Fig. 9 is a corresponding characteristic diagram; and Fig. 10 is afrequency scale to which reference will be made in explaining a certain notation employed.

In Fig. 1 the numeral 11 indicates a source so, 1920. Serial No. 427,392.

of alternating current of varying frequency or of different frequencies superposed, and 12 represents apparatus connected in circuit therewith to which it is desired to admit only those currents having their frequency between certain limiting values. Between 11 and 12 are a plurality of parallel circuits, each comprising an inductance L, a condenser C, and a. resistance R in series. These letters, L, C and R, are also used in the following discussion to indicate the numerical measures of the inductance, capacity, and resistance of the three elements respectively. These values are not the same for the different parallel branches, but they may diff-er in gradation from one branch to the next, for example in the manner that will be pointed outin the explanation that follows. In a special case that will be considered by way of illustration, it will be shown that with twelve parallel branches the impedance varies with the frequency somewhat according to the curve 1 in Fig. 3, though it should be mentioned that the abscissa; in Fig. 3 do not representfrequency, but a function of frequency, as will be fully explained presently.

Of course each branch LCR of Fig. 1 is resonant to a particular frequency 7",, such that The design is such that the values of f, for

mittance y, conductance g, and susceptance b as functions of the resistance R, inductance L, capacity C, and frequency f (where w Qwf.) Thus we have Impedance, .2 \/R (L 6 Resistance, r R

1 Reactance, a; Lw

The above formula for conductance may be established as follows: Let dashes be placed over the letters to indicate corresponding vector values. Then in the conventional complex number notation,

' The real term i It x is the conductance, and substituting for :11 its value as given above, the formula given for conductance g is obtained at once.

When working with circuits or branches connected in series, the resistance, reactance, and impedance are used, but when working with circuits connected in parallel the con ductance, susceptance, and admittance are used. In analytical work the frquency is in some Ways an inconvenient variable, and especially for purposes of graphical representation of the solution of branching networks. I tind that a more convenient way of dealing with these problems involving resonant circuits consists in expressing 2, a, 3 g, and I) as functions of the resistance R, selectance S, and a new variable a, which I shall call the frequency function. Thus x=a RS raumas in which f is the frequency to which the the formulas already given in terms of R, L i

and C. Thus, for example, we may prove the first of the foregoing list of formulas,

In this expression substitute wav for on and substitute for S. Since these steps involve simple algebra, they will be omitted here, but the result will be the formula written out heretofore for 2 in terms of R, L and G. Since all the steps are reversible, this proves the formula for z in terms of a and S. Similarly, the other formulas in terms of a and S may be proved.

Though the function a deduced and defined as above is the function of some particular circuit, it need not be so restricted and may be used as a new variable in place of w or f whether or not there be any circuit involved which is actually attuned to frequency f, and it is in this more general aspect, and as such a new variable, that I have used this function in the present solution of the problem of the system of low impedance circuits for a given frequency band in Fig. 1.

This solution is quite general, except that it requires one-half of the width of the frequency band to be small compared to the medial frequency of the band, a condition to which practically all examples met with in practice may readily be made to conform.-

is small compared to unity.

tervals. Call the frequency f at the midpoint of the range PQ, and since the midpoint of the first interval to the right is a half interval distant, call it f;.. Going on,

consistently with the foregoing the frequency at the midpoint of the second interval to the right from f will be f,, and so on. The frequency at the midpoint of the last interval will be fa, or, more generally,

At the left of the main midfrequ-ency f consistently with the foregoing, we shall. have interval midpoint frequencies f iwf-iw f' a or, more generally for this last value,

From the foregoing it will be seen that. the interval mldfrequency values, such as 'nfi-a 'f-tvfmay be represented generally by the for mula fnm,

where m takes the odd number values from This system of notation can be employed for other functions than frequency. For example, if the midfrequency of a certain interval is values, their respectiv e'inductance and capacity may be designated Lam and

In the particular case when a212, as assumed for Fig 10, and when we have regard to the extreme right-hand interval of the range, viz, the twelfth interval, then these expressions become Li and CH.

In describing the system of Fig. 1, I shall resistances, selectances, and frequency functions of the parallel branches represented respectively by r, s, and or.

Two of the more important forms of the system shown in Fig. 1 are: first, one in which the impedance is small and substantially constant throughout the band; and second, one in which the rate of change of the reactances is negative and substantially constant throughout the band. Of these two forms the former is of more immediate utility, and will be described in some detail by way of an example for all cases.

In the form of the apparatus of Fig. 1 chosen for illustration, there are n parallel branches, all having substantially equal resistances and selectances, but with their frequency functions or varying from branch to branch in arithmetical progression, with common difference selectance S, the condition that it shall be not greater than the reciprocal of A that is As the frequency of each branch is determined by the expression 2 2 flrzg a-mf0 fn-m and if a branch circuit corresponding there- ""2" to has a coil and condenser of appropriate therefore fl-WL 1 n-m 2 1 n-m 4 3 nm 6 When gg- A is small compared to unity as Let S=g Where 0 p2l, and we get always is in any practical case,

I impose on the it crofarads,-

We may now consider a numerical example.

Letf 10", A 1O' ,p= 1, R 10; then L =0.015085 millihenrys, (I 0.15085 mi- I L .=0.010843 millihenrys, C4, 0.16843 microfarads,f 1,1.=1.0275 X10, -f ,t=0.9725 X10 8 100, lt=.0.1 ohm.

The apparent impedance of the filter for currents having frequencies within the as signed frequency band is 0.034v ()llll'lS.

Fig. 3 is a set of characteristic curves for the system of Fig. 1 as developed according to the preceding theory of design. The curve 1 of Fig. 3 represents the impedance for a filter having twelve branches, in which AS:1. Curve 2 in Fig. 2. represents the impedance of a filter for a band of substantially the same width, but having only six branches instead of twelve, and with the resistance and selectance the same as for the twelve-branch filter of curve 1, but in which therefore A-S==2. Remembering that for the comparatively narrow range of frequencies comprehended within the band there is a roughly approximate correspondence in the variation of the frequency f with a it will be seen that the curves 1 and 2 show that the device gives a low impedance over the frequency band and a comparatively high impedance at frequencies a little outside the band. Curves 3 and 4 represent the reciprocals of the susceptances, with sign reversed, for the twelve-branch and sixbranch filters respectively. These curves are introduced here for the reason that they will be convenient to refer to later on. \Vhile these reciprocals of susceptance have the dimensions of reactance, it should be observed that they are not the reactances of the filters.

The greater amplitude of the ripples in curve 2 compared to curve 1 is due to the larger value of the product A-S, while the greater value of the impedance of the sixbranch filter for currents of frequencies within the band is due to the smaller number of parallel paths through which the current may divide in its passage from the generator 11 to the apparatus 12.

The curves 1 and 2 of Fig. 4: are respectiveand 9:2

the passage of currents of and d n e-l ap 42 a) 1.

ly the admittances for the twelve-branch and six-branch filters of Fig. 1. Evidently these curves 1 and 2 of i have as their ordinates the reciprocals of the ordinates of the COFX'GSPODCliHg curves in Fig. 3. Curves 3 and 4 of Fig. 4 are the susceptances of the twelve-branch and six-branch filter respeciively with sign reversed. Curve 1 of Fig. :3 is the conductance of the twelve-branch iilter, for which AS:1. Curve 2 of Fig. 5 represents the susceptance of the same twelvebranch filter. Except for the number of branches and the relation A-S:1 or A-Szi, these curves are quite general in their application, and independent of the particular values asigned for R, S, and w...

A circuit system designed to Present a large impedance to the passage of currents of frequencies within a given band, and only a small impedance for currents outside that band may be constructed of resonant loop circuits as illustrated in Fig. 2. The object of this system is to prevent a band of frequencies from the generator 11 from getting to the apparatus 12 while permitting frequencies higher or lower than the limits of the band. In other words, the system of resonant loop circuits shown in Fig. 2 is designed to offer a higher impedance to currents of frequency between tertain values, but. only a low inipedance to currents of frequency above or below that range.

The treatment of the problem of Fig.2 is in close analogy to that of Fig. 1, so that it will presently be made apparent that the solution for Fig. 1 is available with a modified interpretation as a solution for Fig. 2.

Each resonant loop circuitof Fig. 2 is made up of a condenser C, a resistance R, and inductance L in parallel, and these same letters are employed to indicate the measures of the capacity, resistance, and inductance respectively. It is assumed that the resistance of the coil L may be neglected. To avoid co nfusion with the case ofFig. 1, the various measured quantities of Fig. 2, such as resistances, reactances, etc., will all be indicated, by the subscript 1. Accordingly for a single resonant loop circuit, such as one of these of Fig. 2, we have the following equations:

Corresponding to the transformation employed in connection with Fig. 1, I find it more convenient to throw these expressions into the form l l l l l l wh e re lhis function I call the excludance of the resonant loop circuit. A comparison of these lastexpreesions for 2,, 1",, m,, 1 (/1 and b, for the resonant loop circuits shows that they are the same functions of G X and a that y, g, b, 2, 1', and m are of R, S, and a, respectively for the resonant series branch circuits. Since in the case of the resonant branch circuits of Fig. 1 the conductances and susceptances of the several resonantbranches add each to each as scalar quantities, not vectors, While in the case of the resonant loops of Fig. 2 the resistances and reactances of the several loops add each to each as scalar quantities, not vectors, the problem in Fig. 2 is seen to be the exact analogue of that of Fig. 1, provided we substitute the conductance of the loop for the resistance of the resonant series branch and the excludance of the loop for the selectance of the resonant series branch. Accordingly we may pass over the further steps for the solution of the problem of Fig, 2, and it remains merely to interpret the curves of Figs. 3, 4 and 5 in such a way as to make them applicable to Fig. 2.

Curve 1 of Fig. 3 represents the admittance of the twelve-loop system 01? Fig. 2. Similarly, curve 2 of Fig. 3 represents the admittance of a six-loop system like Fig. 2. The width of the frequency band is taken substantially the same for the two cases of twelve loops and SlX loops. Curves 3 and 4 of Fig. 3 are the corresponding reciprocals of the reactances (with their signs reversed) for curves 1 and 2, These quantities have the same dimensions as susceptances, but they are not the susceptances-of the system of Fig. 2. Curves 1 and 2 of Fig. 4 are the impedances of the twelve-loop and six-loop embodiments of Fig. 2 respectively, and curves 3 and 4 of Fig. 4 are the corresponding reactances (with their signs reversed). Curves 1. and 2 of Fig. 5 are the resistance and reactance respectively of the twelve-loop system of Fig. 2.

In the case of the resonant branch circuits of the filter of Fig. 1, I expressly neglected the eli'ect of the leakage conductance of each condenser, and in the same way for the resonant loop circuits of Fig. 2, I neglected the effect of the resistance of each coil, The criteria determining when this may be done are as follows:

CR X

is negligible compared to unity for each resonant series branch and is negligible compared to unity for each resonant loop.

Now that the two special cases have been considered, the general. case will be readily apprehended, and it will be understood that the foregoing disclosure has been largely by way of ez-ia nple, and that these systems that I have disclosed need not necessarily be constructed respectively of resonant branches and loops conforming to the above criteria. 'l. he general resonant branch circuit is one in which takes the place of R and the general resonant loop circuit is one in wh1ch takes the place of G in the more restricted cases we have considered. If we call these two tunctioi'ls the effective resistance R and effective leakage conductance G, respectively, then the rules given above for the construction of the systems of Fig. 1 and Fig. 2 apply provided the effective resistance and etlective conductance be substituted for the resistance and conductance of the resonant branch and loop circuits respectively. In

practice, the width of the frequency band in will. be substantially unity for all frequencies within the'band, and accordingly we may write for the ellecti've resistance of the series branches, and likewise we may write for the eli'ectire conductance of the loops. Accordingly, the general selectance becomes and the general excludance becomes lVhen it becomes desirable to employ these impedance networks in radio circuits to pro sent an extreme impedance over a certain frequency band, and an oppositely extreme iniipedance outside tl at band, a ditficulty is encountered because whether open aerials or closed aerials are used and whether for transmitting or receiving, they have a pro nounced inherent reactance of their own which must be neutralized throughout the band if the impedance of the circuit is to be maintained approximately constant through out the band. Also when such networks are used in local circuits associated with transmitting and receiving conductors, either in radio transmission or high frequency wire transmission, these localcircuits may have inherent reactan'ces which should be neutralized throughout the band.

Such a neutralization may under many misses of dealing with such a situation is to use a separate device for neutralizing the natural or inherent reactance over the desired fre quency band.

Among the more important cases for which it will be desired to neutralize he reactance, the latter will have one ot three forms La and (r lls. The first two forms may always be reduced to the third torm. hen the reactance is a pure inductance reactance, the addition of a capacity reactance in series will produce the third term, while it the reactance he a pure capacity reactance, the addition of an inductance reactance in series will produce the third form. The third term is, as will be readily appreciated from the earlier part of this specification. that of a resonant circuit having the periodicity (0 Having reduced the reactance ot' the circuit to the form a RS. we then put in additional reactance so chosen as to make the a, ot the resulting resonant circuit correspond to the medial treqnency of the band of frequencies over which the reactance is to be neutralized; we may then add a series o'l loop circuits which will completely neutralize this reactance RS over a band of frequencies corresponding to values oi 01 lt'ron'i A to +A.

For this purpose we may use one or more loop resonant circuits connected in series as illustrated in Fig. 2. \Vhen the hand is narrow and a l'iigh resistance is not objectionable, a single loop circuit may be adetpaats; hut when the band is wide and a high re astancc is to be avoided, a plurality of the e circuits as explained for Fig. 2 should be employed.

The theory of operation of these hand reactanee neutralizers involves the following considen "ions: The reactance of a resonant circuit. in which G i sutiiciently smell. is RS, and the reactance of a loop circuit attuned to the same pc 'iodicity, and in which R is sufficiently small, is

unfit. 1 0 1 In this expression, when afXf is negligibly small compared to unity, the express' sion reduces to and this reaet-ance will exactly neutralize AX =O.2 and RS= 1;

latter equation reducing to Fsi CI c or. L1

where and where C L and G1 are the capacity. 7 inductance, and conductance respectively of the loop. The resistance of this loop throughout the band of. width 2A. will be substantially This single loop band rectance neutralizer is illustrated in Fig. 6, and characteristic curves for it are shown in Fig. 7, where curve 1 is the reactance 113 of the resonant circuit to be neutralized, curve 2 is the reactance of the neutralizing loop circuit, and curve 3 is the resultant reactance of the entire circuit comprising the react-ance neutralizer. When more than one loop circuit is to be used as indicated in Fig. 8, the width of the band is not restricted to those values of @4 of the elemental loops which are negligible compared to unity, but

'the band width may advantageously be broadened to comprehend all values of (1 X of the elemental loops to a Xzl. This is illustrated in Fig. 9 which shows characteristic curves for the network of Fig. '8.

In the three-loop band reactance neutralizer of Fig. 8, the respective loops are tuned to periodicities such that a,: L\a.,:O, and IA. respectively. it will be understood that in Fig. 9 all the ordinates are reactances and the abscissae are values of the frequency function (t Curve 1 is the reactance RS of the given resonant circuit to be neutralized. Curves 2, 3, and 4 are the reactances of the three elemental loops respectively, curve 5 is the sum of curves 2, 3 and 4, and curve 6 is the resultant reactance of the entire circuit as modified by the reactance neutralizer.

Any number of loop circuits may be used in a band reactance neutralizer, and the effect of increasing the number of loops is to increase the width of the band or to diminish the resistance, or both.

It is believed that the foregoing discussion of a few examples of the use of band rcactance ncutralizer will sufficiently indicate their utility in various connections. To carry the particular examples already dis cussed a little further; that is, to make them still more specific, the filament and grid of an audion have been indicated in Figs. 6 and 8. The most effective condition is that in which the conductance of this translating device is made the conductance of a band reactance neutralizer which neutralizes the reactance CXORS, of the resonant circuit with which the translating device is connected. This mode of connection is the most efficient possible. The magnitudes of the reactance of a loop is not affected by the algebraic sign of the conductance G so that the translating device may have a negative conductance in which case it becomes regenerative.

By means of the general method which I have illustrated in the foregoing specification, it will be seen that it is possible to design a circuit such that between 2+1! and az-A laid off on a scale of abscissa, this circuit shall have a circuit function such as rcactance, admittance. etc., corresponding to any given finite single valued, odd or even function of a between those limits, the circuit function being odd or even, accordingas it is resistance. conductance, impedance or admittance on the one hand or reactance or susceptance on the other hand.

What I claim is:

- 1. A circuit comprising a source of elec-' troanotive force, device to which currents are to be applied as generated from said source, and an interposed network, said network comprising a plurality of similar combinations. each combination consistingof two terminals with a resistance, a capacity and an inductance connected alike between said two terminals, the resistances in the several combinations being equal, .all the combinations being connected alike in re spect to the said circuit, the combinations all having the same selectance of value not greater than unity and having their frequency functions in arithmetical progression with a relatively small common difference,

-whereby the network has a substantially uniform impedance over the frequency range corresponding to the said frequency functions and has a widely different impedance outside that frequency range.

2. A circuit comprising a source of electromotive force. a device to which currents are to be applied as generated from said source, and an interposed network, said network comprising a plurality of similar com- Illti binations, each combination consisting of two terminals and a resistance, a capacity and an inductance connected alike between said two terminals, all the combinations being connected alike in said circuit and all having the same sclectancc and having their.

frequency functions in arithn'ietical progres sion with a relatively small common difference, whereby the network offers a substan' tially uniform impedance to currents of the frequency range corresponding to said frequency functions and a widely different impedance to curents of frequencies outside that range.

3. A circuit comprising a source of electromotive force, a device to which currents are to be applied as generated from said source, and an interposed network, said network comprising a plurality of similar combinations, each combination consisting of two terminals and a resistance, a capacity and an inductance connected alike between said two terminals, all the combinations be ing connected alike in said circuit, the combinations having their frequency functions in arithmetical progression with a relatively small common difference and eachliaving its resistance, capacity and inductance proportioned to make the impedance-frequency characteristic of the network of substantially uniform slope over the frequency range corresponding to said frequency functions with a widely different value for the impedance at frequencies utside that range.

4. A circuit comprising a source of electromotive force, a device to which currents are to be applied as generated from said source, and an interposed network, said network comprising a plurality of similar combinations, each combination consisting of two terminals and a resistance, a capacity and an inductance connected alike between said two terminals, the resistances in the several combinations being equal, all the combinations being connected alike in said circuit, and the combinations all having the same selectance.

5. A circuit comprising a source of electromotive force, a device to which currents are to be applied as generated from said source, and an interposed network, said network comprising a plurality of series loops, each loop consisting of a resistance, a capacity and an inductance in parallel, the resistances in the several loops being equal,

all. the loops being connected alike in said circuit, the loops all having the same selectance and having their anti-resonant frequencies approximately in arithmetical progression with a small common difference.

ti. A circuit comprising a source of electromotive force, a device to which currents are to be applied as generated from said source, and an interposed network, said network comprising a plurality of series loops, each loop consisting of a resistance, a capacity and an inductance in parallel, the loops having their frequency functions approximately in arithmetical progression with a relatively small common difference and each loop having its resistance, capacity and inductance proportioned so that the impedance-frequency characteristic of the network shall have a substantially continuous predetermined form.

7. A network con'iprising a plurality of loops connected in series, each loop consisting of a resistance, a capacity and an inductance in parallel. the resistances being equal, the loops all having the same selectance and having their anti-resonant frequencies in arithmetical progression with a relatively small common difference, whereby the network has a low and substantially uniform impedance for all frequencies within the range of said arithmetical progression and a high impedance for frequencies outside that range.

8. A circuit comprising a source of electromotive force, a device to which currents are to be applied as generated from said source, and an interposed network, said network comprising a plurality of similar combinations, each combination consisting of two terminals and a resistance, a capacity and an inductance connected alike between said two terminals, all the combinations being connected alike in said, circuit and all having the same selectance and having their frequency functions in arithmetical progression with a relatively small common difference, the combinations corresponding to consecutive terms of the arithmetical progression having their resistances of nearly the same value.

In testimony whereof, I have signed my name to this specification this 18th day of November, 1920.

JOHN STONE STONE. 

